Add granular DB error types with retry logic

New exceptions: DatabaseBusyError, DatabasePermissionDeniedError,
DatabasePathInvalidError, DatabaseCorruptedError, DatabaseUnavailableError.

open_db creates parent directory if missing. Catches all aiosqlite errors
and maps to specific exception types.

get_db retries up to 3x on locked database with backoff.
Propagates specific exceptions instead of generic HTTPException.

Tests for all new error types and retry behavior.

backend/app/exceptions.py

@@ -473,6 +473,75 @@ class SetupAlreadyCompleteError(ConflictError):
         super().__init__("Setup has already been completed.")
 
 
+class DatabaseBusyError(ServiceUnavailableError):
+    """Raised when the SQLite database is locked or busy after all retries."""
+
+    error_code: str = "database_busy"
+
+    def __init__(self, database_path: str, retries: int) -> None:
+        self.database_path = database_path
+        self.retries = retries
+        super().__init__(
+            f"Database is temporarily busy after {retries} retries."
+        )
+
+    def get_error_metadata(self) -> ErrorMetadata:
+        return {"database_path": self.database_path, "retries": self.retries}
+
+
+class DatabasePermissionDeniedError(ServiceUnavailableError):
+    """Raised when the database file cannot be accessed due to insufficient permissions."""
+
+    error_code: str = "database_permission_denied"
+
+    def __init__(self, database_path: str) -> None:
+        self.database_path = database_path
+        super().__init__("Insufficient permissions to access the database file.")
+
+    def get_error_metadata(self) -> ErrorMetadata:
+        return {"database_path": self.database_path}
+
+
+class DatabasePathInvalidError(ServiceUnavailableError):
+    """Raised when the database directory does not exist or the path is invalid."""
+
+    error_code: str = "database_path_invalid"
+
+    def __init__(self, database_path: str) -> None:
+        self.database_path = database_path
+        super().__init__("Database directory does not exist or path is invalid.")
+
+    def get_error_metadata(self) -> ErrorMetadata:
+        return {"database_path": self.database_path}
+
+
+class DatabaseCorruptedError(ServiceUnavailableError):
+    """Raised when the database file is corrupted."""
+
+    error_code: str = "database_corrupted"
+
+    def __init__(self, database_path: str) -> None:
+        self.database_path = database_path
+        super().__init__("Database file is corrupted.")
+
+    def get_error_metadata(self) -> ErrorMetadata:
+        return {"database_path": self.database_path}
+
+
+class DatabaseUnavailableError(ServiceUnavailableError):
+    """Raised for any other unexpected database error."""
+
+    error_code: str = "database_unavailable"
+
+    def __init__(self, database_path: str, error: str) -> None:
+        self.database_path = database_path
+        self.error = error
+        super().__init__(f"Database is not available: {error}")
+
+    def get_error_metadata(self) -> ErrorMetadata:
+        return {"database_path": self.database_path, "error": self.error}
+
+
 class BlocklistSourceNotFoundError(NotFoundError):
     """Raised when a blocklist source is not found."""